Geomembrane (GM) is a kind of cost-efficient material for pollutant barriers in landfills, while defects can occur during the installation or service periods, resulting in a mixed-type boundary condition (MTBC) at the top surface of the underlying soil layer (SL). In this study, a novel boundary transform method is employed to handle the MTBC problem of axisymmetric transport of organic contaminant through defected GM, and a semi-analytical solution is derived to evaluate the concentration profiles in the spatiotemporal domain. The proposed solution is in the cylindrical coordinates that can incorporate the diffusion and dispersion processes, as well as the concentration condition in the GM defect. The discretization method, integral transforms and corresponding inverse transforms are applied to obtain the semi-analytical solution, which is demonstrated to be effective compared to the numerical results. The model is applied to predict the migration characteristics of organic contaminant in several cases, followed by discussions to evaluate the influencing roles of defect rate, anisotropic coefficient, and segment number. Results indicate that the existence of defects substantially reduces the barrier capacity of the GM layer, and the contaminant migration time varies in several orders of magnitude for different MTBCs.

中文翻译：

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污染物通过有缺陷的土工膜轴对称传输的半解析模型

土工膜（GM）是一种经济高效的垃圾填埋场污染物屏障材料，但在安装或使用期间可能会出现缺陷，导致下伏土层顶面出现混合型边界条件（MTBC）。 SL）。在本研究中，采用一种新颖的边界变换方法来处理有机污染物通过缺陷GM的轴对称传输的MTBC问题，并导出半解析解来评估时空域中的浓度分布。所提出的解决方案采用柱坐标系，可以包含扩散和色散过程以及 GM 缺陷中的浓度条件。应用离散化方法、积分变换和相应的逆变换获得半解析解，与数值结果相比证明是有效的。该模型用于预测几种情况下有机污染物的迁移特征，然后讨论评估缺陷率、各向异性系数和段数的影响作用。结果表明，缺陷的存在大大降低了 GM 层的阻挡能力，并且不同 MTBC 的污染物迁移时间存在几个数量级的差异。